This Ask Me Monday post discusses teaching ideas to use with a renerek.
I ran across an abacus with 2 bars and 10 pearls on each rod; 5 red and 5 white. I know I got this at a conference, and I know I hoped to use it to perhaps improve number sense in my high school freshman. I can’t come up with anything creative that I can do with just the one of them. Any ideas?
Background on Class:
This is an Algebra 1 class where about half of the students have extreme difficulty with basic multiplication and addition facts without a calculator.
The type of abacus you describe is called a renerek. It is generally used in primary grades (K-3) to improve number sense and to teach counting, addition, subtraction, subitizing, and so on. I bought a renerek this year to go with my daughter’s Kindergarten math curriculum. For the readers who want a resource on using the renerek in the primary grades, Amazon has a teaching book called, “Working with the Renerek.”
Ideas for Teaching Math Concepts to Older Students with the Renerek
Evan-Moor has a book called, “Building Math Fluency.” The 4-6+ grade book teaches strategies for solving addition, subtraction, multiplication, and division facts. I used the first grade book with my children and was very pleased with how well it worked for them. CLICK HERE to read my review of the first grade book. CLICK HERE to learn more about the 4-6+ grade book and to view samples on Evan-Moor’s website.
The Building Math Fluency books teach strategies to quickly solve math facts. You can use a renerek to provide a visual representation while teaching a specific strategy (e.g., Tens Partners for addition). For practice, the students can demonstrate the strategy using a renerek. The following math fact strategies ideas with a Renerek are derived from strategies taught in the Building Math Fluency book.
Addition: Tens Partners
In the Tens Partners strategy, students learn all of the combinations that add up to 10 (e.g., 5+5, 1+9, etc.). A renerek may be particularly helpful for teaching and visualizing tens partners as there are 10 beads on a row. The groups of 5 in different colors help students quickly see the numbers without counting each bead. For example, all of the white beads on a row are 5. Seven is 5 white beads and 2 red.
Addition: Doubles Plus One
Another strategy is to learn the doubles (e.g., 2+2=4, 3+3=6, and so on). Once a student knows their doubles, they can learn to recognize doubles plus one.
For example, if the student sees 4+5, they can think the answer is really 4+4+1. Then to solve on the renerek, move the 4 white beads on the bottom to the right and move 4 beads on the top row to the right.
And you get the answer of 9.
Subtraction: Minus 9
Subtracting 9 can be a difficult fact set to master. Rather than memorizing the minus 9 facts, if they child is taught to think that minus 9 is really a number minus 10 plus 1, they will be able to calculate the answer quickly.
For example, 17 minus 9 is more easily calculated if the child thinks of 17-10 first, and then adds one. First take the 10 away on the top row and then add the 1 to the bottom row.
The correct answer of 8 is easily seen with the 5 white beads and 3 red beads. In initial teaching, you could also have the student take 9 away to see that the answer is the same.
Since the Renerek only has 20 beads, it probably isn’t the most practical tool for teaching multiplication facts to high school students. When I teach multiplication, I start with skip counting using the songs from Multiplication Unplugged. Although I own the digital download, I just noticed that the entire selection can be streamed from amazon for FREE with a prime membership (was available on 4/15/19 for free, but may be subject to change without notice).
Younger students may benefit from using the renerek to practice multiplication using skip counting. For example, to calculate 5×7, the student could make 7 on the renerek and then count by 5s with those 7 beads.
Once the concept of multiplication is understood, I teach fact memorization using Times Tales. Times Tales teaches stories in video format to help students memorize the more difficult math facts. A digital version is also available for purchase on the Times Tales website. In addition, Times Tales has an app on iTunes. I haven’t tried the app yet and cannot comment on its quality in comparison to the digital downloads I have previously used.
With high school students, they may think songs or videos are too immature. At the same time, some students might have a lot of success if they are motivated to learn their multiplication facts that will help them calculate their higher level math problems more fluently. Parents may also be willing to buy and/or encourage their freshman to use these resources to build missing math fact skills.
Basic Algebra Problems
Some basic algebra concepts could also be demonstrated and practiced with a renerek. The Hands on Equations curriculum uses manipulatives to teach children to solve linear equations. A renerek can be used in a similar way to represent unknown variables, such as x.
In the equation, 2x + x = x + 8, use the top row to represent the left side of the equation and the bottom bead row to represent the right. For known whole numbers (e.g., 8), either use a 10-sided die like I did in the photograph above, or use a number card.
To balance the equation, take away one x from each side. Now you have 2x = 8.
Divide each side by 2, and you are left with 1x = 4.
Although a renerek is generally used in the primary grades, it can be helpful in teaching math fact calculation strategies and simple algebra to young teens.
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